If the roots of $2x^2+4x-1=0$ are $a$ and $b$ , find $a^2+b^2$ ?

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Answer 1 · 2016-12-11T16:34:20

$a^2+b^2=5$

Sum of roots in a qudratic equation $px^2+qx+r=0$ is $-q/p$ and product of roots is given by $r/p$ .

If roots of $2x^2+4x-1=0$ are $a$ and $b$ , we have

we have $(a+b)=-4/2=-2$ and

$ab=-1/2$

Hence $a^2+b^2=a^2+2ab+b^2-2ab$

= $(a+b)^2-2ab$

= $(-2)^2-2×(-1/2)$

= $4+1$

= $5$

If the roots of 2x^2+4x-1=02x^2+4x-1=0 are aa and bb, find a^2+b^2a^2+b^2?